In operation of a boat in coastal waters, large bays, and rivers, it is frequently desirable to ascertain one's position. This position can be determined by various means which include means independent of dead reckoning plotting or calculations which are subject to error caused by the lack of present knowledge of course, speed and current. The applicant's invention is of such nature. When operating a boat in waters such as those described above, various navigational land marks such as lighthouses, markers, chimneys, spires and tall buildings are often visible. These landmarks are shown on navigational charts of the local areas along with their heights above mean high water.
If two or more navigational landmarks are visible from the boat, the compass bearing of each may be obtained. When converted to true bearings this will yield lines of position which can be plotted on a chart. The intersection of two or more lines of position will give the desired position of the boat.
However, it frequently occurs that only one navigational aid is visible at a given time or, if two or more are visible, they are situated in such a manner that the angular cut of these lines of position will yield a rather large uncertainty in the position determination.
Under these conditions (single line of position) a fix may be obtained by measuring the distance from the boat to the navigational landmark. This will yield a circle of position whose intersection with the line of position, from the object, will result in the boat's position determination.
The distance from a navigational landmark may be measured by different methods. Electronic devices may be used, such as RADAR, but these are costly, bulky and power consuming and are seldom found on small or even moderate size boats.
Another method which can be used (and which is the principle of the instant invention) is to measure the angular subtense of the object (navigational landmark) from the boat and, by means of the appropriate mathematics, determine the distance.
This can be accomplished by means of a sextant which is an angle measuring device. However, to convert the angle measured by the sextant to distance requires special tables and mathematical manipulation which is somewhat laborious and time consuming and also subject to errors. To be specific, the sextant angle must be first corrected for the height of eye (dip table). Then the height of eye must be substracted from the height of the object. These two values are then used to enter Table 9 of H.O. Pub. No. 9 (Bowditch) or equivalent. Since there are two entering arguments, the calculation of distance will (in most cases) require a double interpolation--a time consuming process.
Another method of measuring the angular subtense of an object is by means of a stadimeter. This is an instrument, similar to a sextant, which is constructed so as to permit the user to read distance directly without having to resort to intermediate tables and computations. However, like the sextant, only one mirror is adjustable for the measurement. Because of the rather small angular subtense of most navigational objects (about one or two degrees at the most) this adjustment is extremely small and requires an accurate fine pitch screw which is somewhat costly. Also, most stadimeters are rather limited in range (3 to 5 miles) because their construction is based upon a flat earth. Any scaling to greater distances will result in significant errors due to the earth's curvature and atmospheric refraction.
The sextant, the available stadimeters and the instant invention all measure the angular substense of an object by the same method. This is accomplished by bringing into coincidence at the eye of the user the direct ray from one point (the base of the object or the visible horizon) and the double-reflected ray from the other point (the top of the object). The measured angular subtense is twice the angle between the two reflecting surfaces. In the case of the sextant and the available stadimeters, only one mirror is adjustable, the other being fixed. Here, the rotation of the single mirror is exactly half the angular subtense of the object. Since, in most cases, the object will subtend only one to two degrees or less, the adjustment of the mirror is quite small which requires high mechanical precision.
In the instant invention, the above is accomplished by means of a relatively simple device which is inexpensive and easily manufactured and accomplishes its objectives through movement of mirrors independent of one another with respect to one another. In this case, both mirrors are capable of rotation by means of a common adjustment mechanism. One mirror rotates a slight, but known amount greater than the other mirror. The eye sees two images, a direct and a double-reflected image. The object is then sighted through the instrument. The top of the object viewed through the double-reflected line of sight is made to coincide with the bottom of the object or the horizon viewed through the direct line of sight. This condition of conincidence is achieved by sliding the height adjustment mechanism back and forth as will be explained hereinafter. The mirror rotates through the angles alpha and beta, as which will be explained more fully hereinafter, until the resulting angle matches the angular subtense of the object. The distance of the object is then read directly from the distance scale.